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Factor the difference of two Squares completely m² - 36n 6

Factor the difference of two Squares completely m² - 36n 6

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Title: Factoring the Difference of Two Squares Completely** **Problem:** Factor the expression: \[ m^4 - 36n^6 \] **Steps:** To factor the difference of two squares, recognize the form: \[ a^2 - b^2 = (a + b)(a - b) \] In this expression, identify: - \( a^2 = m^4 \) → \( a = m^2 \) - \( b^2 = 36n^6 \) → \( b = 6n^3 \) Thus, the expression becomes: \[ (m^2)^2 - (6n^3)^2 \] Apply the difference of squares formula: **Answer:** \[ (m^2 + 6n^3)(m^2 - 6n^3) \] This factors the expression completely.
Transcribed Image Text:**Title: Factoring the Difference of Two Squares Completely** **Problem:** Factor the expression: \[ m^4 - 36n^6 \] **Steps:** To factor the difference of two squares, recognize the form: \[ a^2 - b^2 = (a + b)(a - b) \] In this expression, identify: - \( a^2 = m^4 \) → \( a = m^2 \) - \( b^2 = 36n^6 \) → \( b = 6n^3 \) Thus, the expression becomes: \[ (m^2)^2 - (6n^3)^2 \] Apply the difference of squares formula: **Answer:** \[ (m^2 + 6n^3)(m^2 - 6n^3) \] This factors the expression completely.
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Given, m to the power of 4 minus 36 n to the power of 6

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